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A Fast Minimal Residual Algorithm for Shifted Unitary Matrices.
- Source :
- Numerical Linear Algebra with Applications; Nov/Dec94, Vol. 1 Issue 6, p555-570, 16p
- Publication Year :
- 1994
-
Abstract
- A new iterative scheme is described for the solution of large linear systems of equations with a matrix of the form A = ρU + &zetaI, where ρ and ζ are constants, U is a unitary matrix and I is the identity matrix. We show that for such matrices a Krylov subspace basis can be generated by recursion formulas with few terms. This leads to a minimal residual algorithm that requires little storage and makes it possible to determine each iterate with fairly little arithmetic work. This algorithm provides a model for iterative methods for non-Hermitian linear systems of equations, in a similar way to the conjugate gradient and conjugate residual algorithms. Our iterative scheme illustrates that results by Faber and Manteuffel [3,4] on the existence of conjugate gradient algorithms with short recurrence relations, and related results by Joubert and Young [13], can be extended. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 10705325
- Volume :
- 1
- Issue :
- 6
- Database :
- Complementary Index
- Journal :
- Numerical Linear Algebra with Applications
- Publication Type :
- Academic Journal
- Accession number :
- 12785156
- Full Text :
- https://doi.org/10.1002/nla.1680010604